Sen. Joe Manchin, D-W.Va., left, and Sen. Patrick Toomey, R-Pa. arrive for a news conference on Capitol Hill in Washington to announce that they have reached a bipartisan deal on expanding background checks to more gun buyers.

WASHINGTON — Republican opposition is growing to a bipartisan Senate plan for expanding background checks for firearms buyers, enough to put the proposal’s fate in jeopardy. But the measure may change as both sides compete for support in one of the pivotal fights in the battle over curbing guns.

The Senate continued debating a wide-ranging gun control bill Tuesday, with the focus on a background check compromise struck last week between Sens. Patrick Toomey, R-Pa., and Joe Manchin, D-W.Va. Manchin said the vote on that amendment was likely to be delayed to late in the week, a move that would give both sides more time to win over supporters.

The two senators met Tuesday with wounded former Rep. Gabrielle Giffords and her husband, former astronaut Mark Kelly, who have worked in recent months to bolster the gun control drive and are trying to line up Senate support for the effort.

“They’re helping immensely just by being here and talking to our colleagues,” Manchin said after their meeting. “We’re close but we sure need their help.”

President Barack Obama, in an interview with NBC’s “Today” show, urged lawmakers to pay attention to public support for expanding background checks and remember the slayings of 26 schoolchildren and staff at Sandy Hook Elementary School in Newtown, Conn.

“The notion that Congress would defy the overwhelming instinct of the American people after what we saw happen in Newtown, I think is unimaginable,” Obama said in the interview, aired Tuesday. He said it’s a given that the vote is politically difficult for some lawmakers “because the gun lobby is paying attention and has shown no willingness to budge.”

“I think we’ve got a good chance of seeing it pass if members of Congress are listening to the American people,” Obama said.

Underscoring the bargaining under way, the two sponsors seemed willing to consider a change to their deal that would exempt gun buyers from background checks if they live hundreds of miles from licensed firearms dealers, said Senate aides and a lobbyist.

The change might help win support from senators from Alaska and perhaps North Dakota, said the aides and lobbyist, who spoke on condition of anonymity because the discussions were private.

Many consider the Manchin-Toomey compromise the best hope for winning Senate approval to widen the background check system, designed to screen out the severely mentally ill, criminals and others from getting firearms. Background checks are widely considered the heart of the gun control drive.

Background checks are required only for sales handled by licensed gun dealers. The Manchin-Toomey measure would extend that to sales at advertised venues like gun shows and online, while exempting other transactions like those between relatives and friends.

The two senators’ deal doesn’t go as far as Obama wanted, but he has said it would represent progress.

From a group of 16 GOP senators gun control advocates have considered possible allies, at least nine have now said they oppose the background check compromise and one said he is leaning against it.

Combined with the 31 senators who voted against debating the overall gun bill last week, that could bring potential opponents of expanding background checks to 41 — just enough votes to block the Senate from considering the compromise. But in the heated political climate and heavy lobbying certain in the run-up to the vote, minds on both sides could change.

One of those expressing opposition was Sen. Jeff Flake, R-Ariz., who said Monday the measure would cover too many gun transactions.

“It would likely even extend to message boards, like the one in an office kitchen. This simply goes too far,” he posted on his Facebook page.

Flake has been a primary target of pressure from gun control groups. He comes from the same state Giffords represented until she was severely wounded in a 2011 mass shooting in Tucson. In addition, Flake’s senior colleague, Sen. John McCain, R-Ariz., said he is leaning strongly toward supporting the background check plan.

Opponents say expanded checks would violate the Constitution’s right to bear arms and would be ignored by criminals. They are forcing supporters of the background check plan to win 60 of the Senate’s 100 votes, a high hurdle.

Fifty Democrats and two Democratic-leaning senators voted last week to begin debate. If all of them support the Manchin-Toomey plan — which is not guaranteed — they would still need eight additional votes.

So far, three Republicans who backed beginning debate have said they will vote for the Manchin-Toomey plan: Toomey himself and Sens. Mark Kirk of Illinois and Susan Collins of Maine.

Sen. Frank Lautenberg, D-N.J., missed last week’s vote after saying he was suffering from muscle weakness, but spokesman Caley Gray said he hopes to be in the Senate for votes this week.

Two Democrats, both facing re-election next year in GOP-leaning states, voted against beginning the gun control debate last week. Sens. Mark Begich of Alaska and Mark Pryor of Arkansas both said they are still deciding on the Manchin-Toomey plan.